A pentagon has actually 5 sides, and can be made indigenous three triangles, therefore you know what ...

You are watching: If the sum of the interior angles of a polygon is 540 then how many sides does the polygon have

... Its interior angles add up to 3 × 180° = 540°

And as soon as it is regular (all angles the same), climate each edge is 540° / 5 = 108°

(Exercise: make certain each triangle below adds up to 180°, and also check the the pentagon"s internal angles include up to 540°)

The inner Angles the a Pentagon include up come 540°

The basic Rule

Each time we include a next (triangle come quadrilateral, square to pentagon, etc), we add another 180° to the total:


ShapeSidesSum ofInterior AnglesShapeEach Angle
If that is a Regular Polygon (all sides room equal, all angles room equal)
Triangle3180°
*
60°
Quadrilateral4360°
*
90°
Pentagon5540°
*
108°
Hexagon6720°
*
120°
Heptagon (or Septagon)7900°
*
128.57...°
Octagon81080°
*
135°
Nonagon91260°
*
140°
...........

See more: Dog Attack Dream Of Being Attacked By A Dog Attacking You? What Does It Mean To Dream That A Dog Attacks You

...
Any Polygonn(n−2) × 180°
*
(n−2) × 180° / n

So the general dominance is:


Sum of internal Angles = (n−2) × 180°

Each angle (of a continuous Polygon) = (n−2) × 180° / n


Perhaps an example will help:


Example: What about a constant Decagon (10 sides) ?

*


Sum of inner Angles = (n−2) × 180°
= (10−2) × 180°
= 8 × 180°
= 1440°

And because that a regular Decagon:

Each interior angle = 1440°/10 = 144°


Note: inner Angles space sometimes called "Internal Angles"


interior Angles Exterior Angles levels (Angle) 2D forms Triangles square Geometry Index